Appease

 Anon:
No, appease means to do something that you don't really want to do to meet someone else's (usually rude or unreasonable) demands. 
The child was screaming, crying and begging for a piece of candy, so his mother gave him a chocolate drop to appease him.

That is not the definition I read:

Appease: to bring to a state of peace, quiet, ease, calm, or contentment; pacify; soothe: to appease an angry king.

Anonymous to bring to a state of peace, quiet, ease, calm, or contentment; pacify; soothe: to appease an angry king.

Yes. You had better make up your own sentence, we will correct it.
I pray people to appease their angriness.

Alphecca has described one of the meanings, which is the same to word "to indulge". Check your bilingual dictionary,

Indeed, giving the child a chocolate will quiet him for a while, but for how long, do you think?

Well the way I want to use it is as follows, all I want to know is if the word can be used without an object after describing the object.

For example:

"The two men were fighting over the last biscuit, it was very annoying. I quickly grabbed it and ate it myself, perhaps that would make them appease."

Is this proper use of the word?

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No. The two men would be even more annoyed, and they were not even fighting with you. Appease is 'make peace with', not 'make peace between'.
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Anonymous"The two men were fighting over the last biscuit, it was very annoying. I quickly grabbed it and ate it myself, perhaps that would make them appease."

I grabbed and ate the last biscuit but, my actions, instead of appeasing them, only made them turn their aggression on me.
I appeased the men who were fighting over the biscuit by offering them all